Mathematical Sciences: Algebraic K-theory

该奖项支持代数K-理论的研究，特别是关于奇点变种的K-理论的结构和可计算性的研究。本文主要研究K-理论、等上同调与循环同调之间的关系，主要从Etale-Chern特征、割圆迹和二次Chern特征三个方面进行研究。他还将研究亚当斯关于K-理论的运算，着眼于消除关于动机上同调和负K-群的猜想。这项研究涉及到代数K-理论。在广义上，代数K-理论涉及基和向量空间等线性代数概念的演化。这项工作对数论和代数几何具有重大意义，并有望在数学的许多不同领域之间建立令人兴奋的联系。

This award supports research in algebraic K-theory, particularly with regard to the structure and computability of the K-theory of varieties with singularities. The principal investigator will investigate the relationship between K-theory, etale cohomology and cyclic homology, via the etale chern character, the cyclotomic trace and secondary chern character. He also will study the Adams operations on K-theory, with an eye toward vanishing conjectures for motivic cohomology and negative K-groups. This research is concerned with algebraic K-theory. In a broad sense, algebraic K-theory concerns the evolution of concepts from linear algebra such as basis and vector space. This work has significant implications for number theory and algebraic geometry, and promises to make exciting connections between a number of different areas in mathematics.